It's quite common for an illegitimate child to be registered with the mother's surname but known throught her/his life by his/her father's surnam, so there is nothing remarkable in Helen being registered as Anderson but in the census as Clyne. And yes, it is a reasonable conclusion that Helen's father's surname was Clyne.
Finding out which Clyne, however, is not so easy.
Have you got your great-grandmother's marriage or death certificate (or both?) Do they give her father's name and occupation?
Another avenue you could try is the Kirk Session records. These often record unmarried pregnancies, and in most cases the errant father is named. The KS records are in the National Archives of Scotland. They have been digitied, but cannot yet be accessed online, so you either need to go to Edinburgh, or to one of the local archives that has access, or you need to get someone to go and look up the Menmuir KS records for you.